2 cameras with their
optical axes parallel and separated by a distance d.

The
line connecting the camera lens centres is called the
baseline.

Let baseline be perpendicular to the line of
sight of the cameras.

Let the x axis of the three-dimensional
world coordinate system be parallel to the baseline

let the
origin
O of this system be mid-way between the lens centres.

Consider a point (x,y,z), in three-dimensional world
coordinates, on an object.

Let this point have image coordinates
and in
the left and right image planes of the respective cameras.

Let f be the focal length of both cameras, the
perpendicular distance between the lens centre and the image
plane. Then by similar triangles:

Solving for (x,y,z) gives:

The quantity which appears in each of
the above equations is called the disparity.

There are several practical problems with this set up:

Near objects accurately acurately but impossible for
far away objects. Normally, d and f are fixed. However,
distance is inversely proportional to disparity. Disparity can
only be measured in pixel differences.

Disparity is proportional to the camera separation d.
This implies that if we have a fixed error in determining the
disparity then the accuracy of depth determination will increase
with d.

However as the camera separation
becomes large difficulties arise in correlating the two camera
images.

In order to measure the depth of a point it must be
visible to both cameras and we must also be able to identify this
point in both images.

As the camera separation increases so do
the differences in the scene as recorded by each camera.

Thus it
becomes increasingly difficult to match corresponding points in
the images.